Show that for any rational number n, the expression 2n ∙ 4^(n+1) ∙1/8^n is equal to 4.

answer:

step-by-step explanation:

use the fact that a^2-b^2=(a+b)(a-b). in this case a=n+1, b=n-1.

i am using "4|expression" to denote that 4 should divide the expression:

4|[(n+1)^2-(n-1)^2]\implies 4|(n+1+n-1)(n+1-n+1)\implies\\\implies4|2n\cdot2\implies 4|4n \,\,\,\mbox{true for all }n\in n

(b)

same trick

8|[(2n+3)^2-(2n-1)^2]\implies 8|(2n+3+2n-1)(2n+3-2n+1)\implies\\\implies 8|(2n+2)\cdot4 \implies 8|8(n+1)\,\,\,\mbox{true for all } n\in n

the answer   is 200

step-by-step explanation:

this is a problem about poisson probabilities.   i don't know if you've

already studied poisson distributions, or if you have a place to look

to read more about the subject.  

here's how you can see a poisson distribution coming.   when there are

a lot of events that may happen at any time (or any place), and when

you're counting how many of them happen at a particular time (or a

particular place), and each event is independent of the others, then

the result is a poisson distribution.   this is roughly true for the

chocolate chips; one chip being in a cookie has only a small effect on

the probability that another chip will be in the cookie.

once you know you have a poisson distribution, you know a lot.   there

is only one parameter to a poisson distribution, so if you know the

mean, you know everything.   the form of the distribution is

  probability of n chips = {[e^(-x)]*(x^n)} / (n! )

this is a very good question

step-by-step explanation:

i got a hair cut today from my mom not to flex just to flex kim jon un is one rad fellow i'd say you'd need to take the hairline in kinda like a box shape like someone rammed a lego brick into your head. from there you really need to take the top up keeping with that boxy aesthetic, finally coat the whole thing with gel if your country economics are failing or whatever you can just coat it with the starving children's food rations. about 5 orphans per strand is a good ratio. good luck with the fresh cut my dude